Question

A determinant of second order is made up of elements $0$ and $1.$ The number of determinants with non-negative values is

• A. 9
• B. 7
• C. 5
• D. 3
• E. 13

Answer 1

Answer: (E)

There are only three determinants of second order with negative value,
$\left|\begin{array}{cc}0& 1\\ 1& 0\end{array}\right|\left|\begin{array}{cc}0& 1\\ 1& 1\end{array}\right|\left|\begin{array}{cc}1& 1\\ 1& 0\end{array}\right|$
Number of possible determinants with elements $0$ and $1$ are $2^4=16$
Hence, number of determinants with non-negative value is $13$ .